1. Field of the Invention
The present invention relates generally to computed tomographic (CT) imaging apparatus that performs three-dimensional (3D) image reconstruction by processing cone beam measurement data representative of an object, and more specifically, to calculating and storing before imaging operation of the apparatus, image reconstruction information dependant on geometric parameters of the imaging apparatus and required for processing of the acquired measurement data in accordance with a cone beam image reconstruction algorithm. During imaging operation of the apparatus, use of the pre-calculated information greatly speeds up the run-time processing of the image reconstruction algorithm.
2. Description of the Background Art
Recently a system employing cone beam geometry has been developed for three-dimensional (3D) computed tomographic (CT) imaging that includes a cone beam x-ray source and a 2D area detector. An object to be imaged is be scanned, preferably over a 360.degree. angular range and along its length, by any one of various methods: i.e., by rotating the x-ray source in a scan path about the object while the object is being translated, by rotating and translating the source while the object remains stationary, or by rotating the object while one of the source or object is translated. These scanning techniques are all equivalent in that the position of the area detector is fixed relative to the source, and relative rotational and translational movement between the source and object provides the scanning (irradiation of the object by radiation energy). The cone beam approach for 3D CT has the potential to achieve 3D imaging in both medical and industrial applications with improved speed, as well as improved dose utilization when compared with conventional 3D CT apparatus (i.e., a stack of slices approach obtained using parallel or fan beam x-rays).
As a result of the relative movement of the cone beam source to a plurality of source positions (i.e., "views") along the scan path, the detector acquires a corresponding plurality of sets of cone beam projected measurement data (referred to hereinafter as measurement data), each set of measurement data being representative of x-ray attenuation caused by the object at a respective one of the source positions. After acquisition, the measurement data is processed for reconstructing a 3D image of the object.
As compared with the processing required for reconstructing an image when using an x-ray source supplying parallel or fan beams, the processing of the measurement data acquired when using a cone beam source is computationally much more complex. This is because when using a parallel or fan beam source, the measurement data is already directly representative of a 2D Radon transform of a cross-section of the object. However, this is not the case when using a cone beam source. Processing of the measurement data acquired using a cone beam source comprises:
1) conversion of the measurement data to Radon derivative data. This may be accomplished using the techniques described in U.S. Pat. No. 5,257,183 entitled METHOD AND APPARATUS FOR CONVERTING CONE BEAM X-RAY PROJECTION DATA TO PLANAR INTEGRAL AND RECONSTRUCTING A THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY (CT) IMAGE OF AN OBJECT issued Oct. 26, 1993, hereby incorporated by reference,
2) conversion of the Radon derivative data to Radon data at polar grid points using, for example, the technique described in U.S. Pat. No. 5,446,776 entitled TOMOGRAPHY WITH GENERATION OF RADON DATA ON POLAR GRID POINTS issued Aug. 8, 1995, also hereby incorporated by reference, and
3) performing an inverse 3D Radon transformation of the Radon data using known techniques, such as those described in detail in the forenoted U.S. Pat. No. 5,257,183 for reconstructing image data that, when applied to a display, provides a view of the 3D CT image of the object.
As generally described in the forenoted U.S. Pat. No. 5,257,183, in order to provide a complete set of measurement data for accurate 3D (and even 2D) imaging of an object (or a region of interest in an object), it is necessary to satisfy completeness criteria. These criteria are well known, and are described in detail, for example, by Smith, B. D., in the publication "Image Reconstruction From Cone-Beam Projections, Necessary and Sufficient Conditions and Reconstruction Methods", IEEE Transactions Medical Imaging, MI-4 (1985), pp. 14-25. Basically, what is required is that any plane passing through the object or region of interest must intersect the scan path at one or more locations. The completeness criteria are also discussed in U.S. Pat. No. 5,383,119 entitled METHOD AND APPARATUS FOR ACQUIRING COMPLETE RADON DATA FOR EXACTLY RECONSTRUCTING A THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY IMAGE OF A PORTION OF AN OBJECT RADIATED BY A CONE BEAM SOURCE issued on Jan. 17, 1995, hereby incorporated by reference. Additionally, this patent notes that the acquired data set is complete only if it can be processed so as to provide data at every point in the Radon space of a so-called "region of support". The "region of support" topologically corresponds to the field of view occupied by the region of interest of the object in real space. The Radon data is typically acquired by exposing the entire object within the field of view to an irradiating source.
As described in the forenoted U.S. Pat. No. 5,383,119, 3D image reconstruction techniques have difficulties imaging objects and regions which have a rather long or tall dimension. Generally, the detector must have a height and width large enough to cover the height and width of a projection of the object or region of interest on the detector, otherwise, some x-ray data would be missing. If the height or length of an object or region of interest is great, it is often impractical or difficult to obtain a detector array with sufficient height to obtain complete measurement data from the object or region of interest.
Sufficient filling of the Radon space by apparatus having various scanning trajectories (paths) and using an area detector which has a height that is less than the height of the region of interest being imaged are known for performing an exact image reconstruction. For example, in the above-noted U.S. Pat. No. 5,383,119, a rather complex technique is described for manipulating the acquired cone beam data so as to discard and recover data, as appropriate, so that only measurement data directly attributable to the region of interest is used for image reconstruction. In U.S. Pat. No. 5,463,666 entitled HELICAL AND CIRCLE SCAN REGION OF INTEREST COMPUTERIZED TOMOGRAPHY issued Oct. 31, 1995, hereby incorporated by reference, a cone beam CT imaging system is disclosed in which a region of interest portion of an object can be imaged without blurring or artifact introduction from imaging portions of the object not within the region of interest. A controllably movable source and relatively small area detector are controlled so as to define a scan path consisting of a central spiral portion having one circle portion at each end of the spiral portion which is level with upper and lower boundaries, respectively, of the region of interest. The switch from a spiral path to a circular path is necessary in order to obtain complete cone beam data at the upper and lower boundaries of the region of interest without blurring caused by imaging portions of the object that are outside the region of interest, as described in greater detail in the forenoted U.S. Pat. No. 5,463,666.
U.S. Pat. No. 5,463,666 also describes a data combination processing technique useful in a 3D CT imaging system having a relatively small area detector. Briefly, to determine the value of each point in Radon space, measurement data acquired from each of several different source positions must be individually processed, each individual processing contributing a fractional amount to the final determination of the value.
Although the techniques noted above describe the theory for exactly reconstructing an image using cone beam measurement data, a practical implementation of the processing turns out to be quite problematic. Not only is the amount of measurement data to be processed very large and rapidly acquired, but the calculations required on the acquired data are quite complex. For example, if one decides to reconstruct an object with 200.times.200.times.200=8.multidot.10.sup.6 (voxel=volume element of the object), for good quality one needs to obtain the object's 3-D Radon transform with a multiple (e.g., 4) amount of Radon samples, i.e., 32.multidot.10.sup.6 samples, and then perform the Radon inversion. The most computationally expensive part of the object reconstruction is the calculation of the Radon derivative date (step 1 noted above). As noted in detail in the forenoted U.S. Pat. No. 5,463,666, measurement data from several source positions typically contribute to each Radon sample by way of data combination, thus one needs to calculate about 100.multidot.10.sup.6 line integral derivatives. Each line integral derivative requires the calculation of 200.multidot.10.sup.6 single line integrals, since one uses the difference between two closely spaced line integrals to calculate a single line integral derivative. However, before one can perform these line integral derivative calculations, one has to compute for each Radon sample which source positions will provide the measurement data that must be processed, and determine the lines on the measurement data along which the integration must be performed. These latter determinations involve highly nonlinear calculations and are therefore computationally costly. In order to compute the contributing source positions, one has to intersect the source scanning path with the Radon integration plane as explained in the forenoted U.S. Pat. No. 5,463,666. When using a spiral scan path, this requires the solution of transcendental equations, which are computationally expensive. Furthermore, in addition to determining the lines on the measurement data along which the integration must be performed, one also has to calculate the appropriate end points of those lines for data combination purposes and region-of-interest masking. The complexity of these above-noted calculations leads to severe bottlenecks in processing of the measurement data, so as to prevent rapid and efficient image reconstruction.
Additionally, since image reconstruction requires processing of Radon space data, but the data being acquired during the imaging operation of the apparatus is cone beam projected measurement data, the run-time (imaging operation) processing of the measurement data results in fragmentary development of the Radon data, thereby adding further complexity to the already severe processing difficulties.
It would be desirable to provide a method and apparatus for processing of the cone beam measurement data in a manner that reduces the above described computational complexities and difficulties, thereby allowing a more efficient implementation of an exact cone beam reconstruction algorithm.
Although the above-noted problems are already known, so far experts have only devised techniques for reducing the amount of measurement data that is to be processed. For example, U.S. Pat. Nos. 5,461,650 and 5,333,164 by Kwok C. Tam are representative of some of these prior art techniques. U.S. Pat. No. 5,461,650 entitled METHOD AND SYSTEM FOR PRE-PROCESSING CONE BEAM DATA FOR RECONSTRUCTION FREE OF INTERPOLATION-INDUCED ARTIFACTS A THREE DIMENSIONAL COMPUTERIZED IMAGE, issued Oct. 24, 1995, is representative of "masking" techniques wherein the amount of measurement data that is required for image reconstruction processing is truncated by defining areas on the detector array from which measurement data is to be discarded. U.S. Pat. No. 5,333,164 by Mr Kwok Tam entitled METHOD AND APPARATUS FOR ACQUIRING AND PROCESSING ONLY A NECESSARY VOLUME OF RADON DATA CONSISTENT WITH THE OVERALL SHAPE OF THE OBJECT FOR EFFICIENT THREE DIMENSIONAL IMAGE RECONSTRUCTION, issued Jul. 26, 1994, is representative of techniques for truncating the image reconstruction processing by selectively retaining for further processing only those Radon data points that are in the objects' Radon region of support. Although such truncations of the measurement data or the Radon data points results in an overall improvement in the speed of reconstructing an image, they do so by discarding data so it is not processed, not by improvement in the speed or efficiency of the processing of the actual measurement data that develops contributions to the final reconstruction of the image.
It would be desirable to provide an improvement in the speed or efficiency of the actual processing of the measurement data that develops contributions to the final reconstruction of the image.